On the subinvariance of uniform domains in Banach spaces



: Huang M, Vuorinen M, Wang X

Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE

: 2013

: Journal of Mathematical Analysis and Applications

: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

: J MATH ANAL APPL

: 2

: 407

: 2

: 527

: 540

: 14

: 0022-247X

DOI: https://doi.org/10.1016/j.jmaa.2013.05.046


Suppose that E and E' denote real Banach spaces with dimension at least 2, that D subset of E and D' subset of E' are domains, and that f : D -> D' is a homeomorphism. In this paper, we prove the following subinvariance property for the class of uniform domains: suppose that f is a freely quasiconformal mapping and that D' is uniform. Then the image f (D-1) of every uniform subdomain D-1 in D under f is still uniform. This result answers an open problem of Vaisala in the affirmative. (C) 2013 Elsevier Inc. All rights reserved.



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